Sending support to all of you. I have zero experience with tonsilectomies, but it sounds very painful (the after care anyway).
I think I would let the issue go about the nurse assuming the gp precribes her medications. There are, in fact, many people who do have their medications monitored and prescribed through their gp. If you need to mention it, mention it, but then let it go.
Regarding the smoking - I'd do the nicorette gum when she becomes desperate. It seems to me the main concern over her smoking one week prior to the surgery is that it is an irritant and could cause some tissue to be raw or irritated and make the surgery a little more difficult. From what I've read and heard, tonsilectomies are already risky for an adult so not smoking just seems to me like a given. However, chewing nicorette gum is not supposed to cause the same irritation in the throat. Or, alternatively, there is the patch. Did they give you a specific reason why she can't smoke? Poor kid. If my difficult child had to go cold turkey PLUS come off her medications like that, we'd all be a mess.
Hugs, hang in there.